Private mortgage insurers accounted for 36% of U.S. mortgage insurance written in the second quarter – their biggest quarterly share of the market since 2008 – according to the report, citing data provided by Royal Bank of Scotland.

And their market share is expected to grow as home prices appreciate and their main competitor, the Federal Housing Administration, charges higher premiums.

Making these mortgage insurers all the more attractive to investors is the fact that they have basically cornered the private market by acquiring the rights to all the existing mortgage insurance platforms, according to the report. Thus, any company seeking to enter the market would have to build its own platform and come up with roughly $200 million to $400 million in capital, according to the report.

What's more, a new insurer would need approval from individual states to write new business, as well as the endorsement of government-sponsored enterprises Fannie Mae and Freddie Mac – a process that can take up to a year.